How Do You Solve This Complex Math Problem Step-by-Step?

[kuahji]

Can't figure out how the example in the book is getting from one step to the next.

Here's the problem
2(8+216/x)(-216/x^2) + 2(x+27) = 0

The next step
(x+27)(1-1728/x^3) = 0

First thing I did was divide out the two & got
(8+216/x)(-216/x^2) + (x+27) = 0
Then I multiplied out the left part
-1728x^-2 + 46656x^-3 + (x+27) = 0
This got me nowhere it seems.
Then I tried to find a common denominator
-1728x-46656/x + (x+27) = 0
this is what I got when I multiplied it out & still nowhere it seems. Any help would be appreciated.

 

[Integral]

Can't figure out how the example in the book is getting from one step to the next.

Here's the problem
2(8+216/x)(-216/x^2) + 2(x+27) = 0


The next step
(x+27)(1-1728/x^3) = 0

Nope. This is wrong, so all that follows is also wrong.

Next step:

$$\frac {- 8 (216)} {x^2} - \frac {216^2} {x^3} + (x+27) =0$$

now multiply through by $x^3$ to get:
$$-8(216)x - 216^2 + x^3 (x+27) = 0$$
now you should be able to continue.

 

[Architeuthis Dux]

I understand your frustration when faced with a difficult math problem. However, it is important to approach the problem systematically and carefully in order to find the next step. Let's break down the given problem and see if we can find a solution.

First, let's focus on the left side of the equation, which consists of two terms: 2(8+216/x)(-216/x^2) and 2(x+27). We can simplify the first term by multiplying the two brackets together, which gives us -1728/x^3. Now, we can rewrite the left side of the equation as -1728/x^3 + 2(x+27).

Next, we can try to find a common denominator for these two terms. The common denominator for -1728/x^3 and 2(x+27) would be x^3. This means we need to multiply -1728/x^3 by x^3/x^3, which gives us -1728x^3/x^3. And for 2(x+27), we need to multiply by x^3/x^3, which gives us 2x^3(x+27)/x^3.

Now, we can combine the two terms with the same denominator and get -1728x^3 + 2x^3(x+27)/x^3. This can be simplified to -1728x^3 + 2x^4 + 54x^3. This gives us the same left side as the next step in the book: (x+27)(1-1728/x^3).

It is important to carefully follow the steps and check for any mistakes along the way. Sometimes, a small error can lead to confusion and frustration. I hope this helps you in solving the problem. Remember to always approach a problem with a clear and logical mindset. Keep practicing and you will eventually become more confident in your math skills.